On Symbolic-Numeric Solving of Sine-Polynomial Equations

This paper deals with the localization of all the real roots of sine-polynomials. D. Richardson (1991, in ``effective Methods in Algebraic Geometry,'' pp. 427 440, Birkha user, Basel) has already studied this type of analytic function. He showed how to find the number of real roots in a bounded interval. Here we propose an algorithm which determines whether a sine-polynomial has a finite number of real roots or not. Moreover in the finite case we construct an explicit interval containing all of them. We also construct a generalized exclusion method to find all the real roots in a bounded interval and we adapt it to the infinite case. 2000 Academic Press